Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063353 | C2 | semidirect |
| 2. C2×M16×D43 | C2 | semidirect |
| 3. #14583411 | C2 | semidirect |
| 4. C2×#13063300 | C2 | semidirect |
| 5. #14583153 | C2 | semidirect |
| 6. #14583146 | C2 | semidirect |
| 7. #14583136 | C2 | semidirect |
| 8. #14583129 | C2 | semidirect |
| 9. #14582903 | C2 | semidirect |
| 10. #14582898 | C2 | semidirect |
| 11. C43×#428 | C2 | semidirect |
| 17. C2×#10621873 | C22 | semidirect |
| 18. C2×D344 | C22 | semidirect |
| 20. C2×#10621872 | C22 | semidirect |
| 22. C2×C8×D43 | C22 | semidirect |
| 24. #13063305 | C22 | semidirect |
| 25. #13063305 | C22 | semidirect |
| 30. #13063300 | C22 | semidirect |
| 31. #13063300 | C22 | semidirect |
| 36. #13063248 | C22 | semidirect |
| 37. #13063245 | C22 | semidirect |
| 38. #13063245 | C22 | semidirect |
| 39. #13063245 | C22 | semidirect |
| 43. #107×C43 | C22 | semidirect |
| 44. #106×C43 | C22 | semidirect |
| 71. M16×C43 | D4 | semidirect |
| 135. C8×C43 | C2×D4 | semidirect |
| 154. C2×D43 | AGL(1,ℤ/8) | semidirect |
| 181. #428 | D43 | semidirect |
| 184. C43 | #3055 | semidirect |
| 212. #107 | C2×D43 | semidirect |
| 213. #106 | C2×D43 | semidirect |
| 248. M16 | D172 | semidirect |
| 309. C8 | C2×D172 | semidirect |